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What Is Applied Category Theory? (2018)

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Re: What Is Applied Category Theory? (2018)

#31

Post by platz »

johndoe42377 wrote: post #30

Just a nice set of ideas to be used for social signalling. In with type systems, a typeclass is all you need. The mantra is "to be an X (being substituted for an X) is to be able to perform (implement) such and such actions (or have this or that biochemical properties). It is that general, that deep, it could be even seen in molecular biology. Category theory, on the other hand, is just a few nested abstract concepts…

There are a lot of claims made to try to apply CT to programming; I agree most of that effort is overhyped.

But CT in general has nothing to do with programming, it's proper role is in pure mathematics

Re: What Is Applied Category Theory? (2018)

#32

Post by threatofrain »

jbotz wrote: post #23
Ceezy wrote: post #20

If anybody interested the best book to learn the category theory: https://www.maths.ed.ac.uk/~v1ranick/papers/maclanecat.pdf

Why do you think this is the best book? And would someone's background, or lack thereof, in other fields of mathematics not have a bearing on that assessment?

If someone lacks interest in math I’m not sure category theory makes sense even in the FOMO way.

Re: What Is Applied Category Theory? (2018)

#33

Post by user-the-name »

newswasboring wrote: post #24

Category Theory is one of those things which I know are important and has applications in many engineering fields. I also have an intuition that its obviously because things need to flow into each other and composability is how we achieve that. But man, whenever I try to get into this I feel like someone is hitting me on the head with equations.

Maybe for a value of "has applications" that doesn't necessarily include anyone actually applying it.

As a generalisation, I don't think anyone by people into category theory actually cares about or applies category theory.

Re: What Is Applied Category Theory? (2018)

#34

Post by [deleted] »

user-the-name wrote: post #33
newswasboring wrote: post #24

Category Theory is one of those things which I know are important and has applications in many engineering fields. I also have an intuition that its obviously because things need to flow into each other and composability is how we achieve that. But man, whenever I try to get into this I feel like someone is hitting me on the head with equations.

Maybe for a value of "has applications" that doesn't necessarily include anyone actually applying it. As a generalisation, I don't think anyone by people into category theory actually cares about or applies category theory.

[deleted]

Re: What Is Applied Category Theory? (2018)

#35

Post by bikenaga »

Ceezy wrote: post #20

If anybody interested the best book to learn the category theory: https://www.maths.ed.ac.uk/~v1ranick/papers/maclanecat.pdf

Mac Lane was one of the founders of category theory - see for example:

"General Theory of Natural Equivalences" - Samuel Eilenberg and Saunders MacLane. Transactions of the American Mathematical Society, Vol. 58, No. 2, (Sep., 1945), pp. 231-294

His "Categorical algebra" paper from 1964 is open-access:

https://projecteuclid.org/euclid.bams/1183526392

When his book came out it was the standard work for a while. I think some of the terminology he uses is no longer standard, and there are now many very good modern introductions. But his book is still a pretty good read, primarily because he was a wonderful writer with a very distinctive style.

That said, the examples (given the time the book was written) are almost exclusively mathematical. The proofs and exercises are usually not difficult, but at a high level of abstraction (not surprisingly).

Re: What Is Applied Category Theory? (2018)

#37

Post by myWindoonn »

xelxebar wrote: post #14
kbr wrote: post #4

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length. The author's blog [1] has more of this style and has r…

Not addressing your question, but the Yoneda Lemma is kind of a charlatan. On first reading, it seems magical and deep, but once you grok the proof, it feels like a relatively trivial observation. The whole thing is just about arrow composition! In a way, once you're on the other side, the Yoneda Lemma feels a bit like a checkpoint during the accimatization period where your brain gets used to thinking in categories…

Yoneda just says that we may exchange an object for all of the arrows which point to (dually, from) it. This is extremely deep; it is rather surprising that objects and arrows would have such a duality or exchange!

Re: What Is Applied Category Theory? (2018)

#38

Post by bordercases »

johndoe42377 wrote: post #30

Just a nice set of ideas to be used for social signalling. In with type systems, a typeclass is all you need. The mantra is "to be an X (being substituted for an X) is to be able to perform (implement) such and such actions (or have this or that biochemical properties). It is that general, that deep, it could be even seen in molecular biology. Category theory, on the other hand, is just a few nested abstract concepts…

Hi Karma.

Re: What Is Applied Category Theory? (2018)

#39

Post by Koshkin »

threatofrain wrote: post #32
jbotz wrote: post #23

Earlier quoted context omitted.

Why do you think this is the best book? And would someone's background, or lack thereof, in other fields of mathematics not have a bearing on that assessment?

If someone lacks interest in math I’m not sure category theory makes sense even in the FOMO way.

To someone who is not interested in math per se but rather in its applications to engineering, category theory, too, has something to offer.

Re: What Is Applied Category Theory? (2018)

#40

Post by newswasboring »

user-the-name wrote: post #33
newswasboring wrote: post #24

Category Theory is one of those things which I know are important and has applications in many engineering fields. I also have an intuition that its obviously because things need to flow into each other and composability is how we achieve that. But man, whenever I try to get into this I feel like someone is hitting me on the head with equations.

Maybe for a value of "has applications" that doesn't necessarily include anyone actually applying it. As a generalisation, I don't think anyone by people into category theory actually cares about or applies category theory.

Shouldn't it be easier to explain a general concept than a specific one? The only reason I can think of why this isn't happening is because you need to learn a large amount of information before any of the category theory stuff can be applied in real life. But honestly speaking, that can't be true because languages like Haskell exist and isn't that on the whole programming using category theory? (I am be completely wrong about this).

OTOH it can also be just a pedagogy issue. That nobody has figured out how to condense it into an undergraduate level so working engineers can grasp basics.

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